Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Question
Calculate the summation
![The expression shown in the image represents a mathematical summation:
\[
\sum_{i=4}^{n} (-2i^2 + 2i + 2n^2 + 2n) =
\]
This sum begins at \(i = 4\) and runs to \(n\).
- **\(-2i^2\)**: This term involves the square of the index variable, multiplied by \(-2\).
- **\(2i\)**: This linear term is positive and increases proportionally with \(i\).
- **\(2n^2\)**: This constant term, relative to \(i\), involves the square of the variable \(n\), multiplied by 2.
- **\(2n\)**: This term is also constant with respect to \(i\) and is dependent on the value of \(n\).
The summation computes the total value of these expressions as \(i\) takes each integer value from 4 to \(n\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc5ac1678-3f3b-440a-b3b5-846319a7a56a%2F5b25e790-7548-4de6-b419-07303609d087%2Fmulmil_processed.png&w=3840&q=75)
Transcribed Image Text:The expression shown in the image represents a mathematical summation:
\[
\sum_{i=4}^{n} (-2i^2 + 2i + 2n^2 + 2n) =
\]
This sum begins at \(i = 4\) and runs to \(n\).
- **\(-2i^2\)**: This term involves the square of the index variable, multiplied by \(-2\).
- **\(2i\)**: This linear term is positive and increases proportionally with \(i\).
- **\(2n^2\)**: This constant term, relative to \(i\), involves the square of the variable \(n\), multiplied by 2.
- **\(2n\)**: This term is also constant with respect to \(i\) and is dependent on the value of \(n\).
The summation computes the total value of these expressions as \(i\) takes each integer value from 4 to \(n\).
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